Sensors for accurately measuring physical, chemical and electrical properties of materials and systems are important in science and engineering. Sensors are needed for analysis in heat and mass transfer processes, fluid and solid mechanics, geophysical and seismic sciences, biologics, health care, and the defense and national security arenas. Applications of sensors include system operational health management, inverse analysis, signature discrimination, industrial process control, quality improvement in materials processing and property measurements, and constitutive modeling.
In addition, calculations of the rate of change of physical, chemical and electrical properties are a valuable analytical tool in, for example, evaluation of thermal processes for estimating instantaneous rate of heat flux at a sensor location, or estimation of heat flux at a location different from the sensor location, such as by use of inverse methods. Calculations of thermal rate change are also useful for thermal property measurement and phase transition identification of new materials. Estimations of temperature changes are helpful for better control of thermal processes, remote sensing and advanced tracking based on rate measurements from various optical sensors and so on.
Heat transfer analysis often involves the precise measurement of temperature to obtain heat flux. Heat fluxes and heating/cooling rates are of special concern owing to their involvement in aerospace, defense and nuclear applications, such as re-entry (arc-jet) and direct energy impingement applications. In such applications, a thermocouple is typically mounted on the surface of a plate exposed to a high incoming heat flux. In these applications, data differentiation is typically used for the diagnostic and predictive processes.
Property rate change information may also be used in diagnostic and predictive analyses in solid and fluid mechanics, and pressure and seismic analysis. These analyses are needed in fire metrology, aerospace, heat treatment, defense and homeland security applications. Extracting reliable derivative data is critical to many diagnostic and predictive processes.
Table 1 lists several application areas wherein the availability of voltage rate-based measurement technology has been deficient.
TABLE 1Application0th-Derivative2nd.3rd.AreaPrimitive VariableDerivativeDerivativeDerivativeUtilityMechanical Vibrationsx(t) displacement  dx  dt            d      2        ⁢    x        dt    2              d      3        ⁢    x        dt    3  Mechanical system analysis, modal analysis, source function reconstruction ElectricalV(t) voltage  I  =      c    ⁢          dv      dt      Electrical system analysis and responses ThermalT(t) Temperature q″(t) Heat flux1      dT    dt    *          ⁢            dq      ″        dt    *                    d        2            ⁢      T              dt      2        *          ⁢                    d        2            ⁢              q        ″                    dt      2        *Surface analysis, embedded analysis (inverse), and property evaluation for health management for real-time analysis. Stress- Strainε(t) strain σ(t) stress            d      ⁢                          ⁢      ε        dt    *          ⁢            d      ⁢                          ⁢      σ        dt    *      Constitutive    ⁢                  ⁢    relations        development    ,                  e        .        g        .                                  ⁢        creep            ⁢                          ⁢      and            stress    ⁢                  ⁢    relaxation              σ      +      τ        =                            d          ⁢                                          ⁢          σ                dt            =                          ⁢                                    E            a                    ⁢          ε                +                              (                                          E                a                            +                              E                m                                      )                    ⁢          τ          ⁢                                    d              ⁢                                                          ⁢              ε                        dt                               PressureP(t) pressure      dP    dt    *Failure and safety analysis ConcentrationC(t) Concentration      dC    dt    *Concentration gradient for biological sensors1q″(t) is expressed in Watts/unit area.
Accurate measurements of parameters identified with an asterisk (*) in Table 1 have generally been particularly difficult to acquire. Typically such measurements are calculated by sampling the associated primitive variable over time and then applying various smoothing algorithms to infer the underlying function, and then mathematically differentiating the function with respect to time to estimate the derivative values. One of the principal impediments to this process is electronic noise present in the primitive variable measurements. Off-the-shelf sensors are often perceived to be accurate without a clear understanding of how the high frequency/low amplitude noise affects the outcome of the numerical method.
Even if the noise problem is minimized it would be preferable to acquire measurements of the derivative values in real time. Ideally, real-time rates would be measured rather than estimated, thereby eliminating the numerical differentiation step from data analysis. However, real-time measurement of physical, chemical and electrical property rate change has been an elusive inverse problem. The interplay between the source of data and the implemented numerical scheme is difficult to account for in these inverse studies.
The number of transient studies continues to increase and yet most measurements are taken using steady-state devised sensors. The trend toward investigating transient (e.g., lasers) problems containing several time scales and interactive events are on the increase. However, developing purely mathematical solutions to physical problems requiring stabilization methods often cannot be applied to real-world problems. As a result of these various difficulties, measurements of rate data are generally more inaccurate and less timely than desired. What are needed therefore are improved devices and methods for acquiring time rate measurements of physical, chemical and electrical properties.